2025-07-13 15:23:24 -04:00
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2025-07-16 00:32:06 -04:00
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2025-07-13 15:23:24 -04:00
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2025-07-13 15:23:24 -04:00
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2025-07-16 00:32:06 -04:00
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2025-07-13 15:23:24 -04:00
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2025-07-16 00:32:06 -04:00
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<title>Mayan Calendar</title>
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2025-07-13 15:23:24 -04:00
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2025-07-16 00:32:06 -04:00
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<a class="navbar-brand" href="#">Mayan Calendar</a>
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<a class="nav-link" href="#explanation">Explanation</a>
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2025-07-16 00:32:06 -04:00
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<a class="nav-link" href="https://frcal.qt.ax">French Republican Calendar</a>
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2025-07-13 15:23:24 -04:00
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<a class="nav-link" href="https://jcal.qt.ax">Julian Calendar</a>
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<a class="nav-link" href="https://gcal.qt.ax">Gregorian Calendar</a>
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<h2 id="explanation">Explanation</h2>
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<div class="card">
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<div class="card-body">
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<h4 class="card-title">What is this?</h4>
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<p class="lead">This is an attempt to render the <a href="https://en.wikipedia.org/wiki/Maya_calendar">Mayan
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calendar</a> in a more familiar “monthly” calendar format.</p>
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<p>The idea of a monthly calendar is sort of alien to the Maya, who used two cycles to track the date and
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a modified base-20 numbering system to track the exact date:</p>
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<ul>
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2025-07-18 03:18:29 -04:00
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<li>The <a href="https://en.wikipedia.org/wiki/Tzolk%CA%BCin"><strong>Tzolkʼin</strong></a>
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cycle, which is a 260-day cycle based on combining 20 day names with 13 numbers, used for religious
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and ceremonial events and for divination;
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</li>
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<li>The <a href="https://en.wikipedia.org/wiki/Haab%CA%BC"><strong>Haabʼ</strong></a> cycle, which is a
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365-day cycle consisting of 18 “months” of 20 day each, plus 5 days at the end of the
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year known as the <em>Wayebʼ</em>;
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</li>
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<li>The <a href="https://en.wikipedia.org/wiki/Mesoamerican_Long_Count_calendar"><strong>Long
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Count</strong></a>, a modified base-20 system used to represent the number of days since the
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mythical date of creation, which is August 11, 3114 BCE in the proleptic Gregorian calendar or
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September 6, 3114 BCE in the proleptic Julian calendar. It is typically represented as five numbers
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separated by dots, with each number counting from 0 up to 19, except for the second last number,
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which counts from 0 to 17.
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</li>
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</ul>
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2025-07-18 03:18:29 -04:00
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<p>Since the <em>Haabʼ</em> is the closest equivalent to months in the Mayan system, this calendar
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application is based on the <em>Haabʼ</em>. This poses a problem, as in the Mayan system, the Long Count
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is used to track the absolute date and the cycles of <em>Tzolkʼin</em> and <em>Haabʼ</em> are
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unnumbered. To mitigate this issue, we attempt to number the <em>Haabʼ</em> cycles, with the date of
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creation in cycle 0.</p>
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2025-07-13 15:23:24 -04:00
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</div>
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</div>
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<div class="card">
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<div class="card-body">
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2025-07-18 03:22:31 -04:00
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<h4 class="card-title">How does Tzolkʼin work?</h4>
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<p class="lead">The Tzolkʼin is composed from two concurrent cycles—the number 1 to 13, and a list of
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20 day names.</p>
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<p>The day name are: Imix, Ikʼ, Akʼbʼal, Kʼan, Chikchan, Kimi, Manikʼ, Lamat, Muluk, Ok, Chuwen, Ebʼ, Bʼen,
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Ix, Men, Kibʼ, Kabʼan, Etzʼnabʼ, Kawak, and Ajaw.</p>
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<p>Note that the day name and number cycles are completely independent and advance concurrently. This means
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that 1 Imix is followed by 2 Ikʼ and so on. There is no definite start or end to this cycle, but day
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names repeat every 260 days, which is the least common multiple of 13 and 20.</p>
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</div>
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</div>
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<div class="card">
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<div class="card-body">
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<h4 class="card-title">What's so special about this version?</h4>
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<p class="lead">Most versions of the calendar floating around doesn't use the original definition above.</p>
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<p>Most versions uses the so-called <em>Romme</em> method for leap years, using the same leap year rules as
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the Gregorian calendar, i.e. every year divisible by four, except century years not divisible by 400.
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This method might make sense, except years 3, 7, and 11 were leap years under the original rules and
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were observed as such in real life, but the <em>Romme</em> method instead makes years 4, 8, 12 leap
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years instead.</p>
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<p>This version uses the original rules. The <a href="https://ssd.jpl.nasa.gov/planets/eph_export.html">JPL's
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DE440 and DE441 ephemerides</a> were used to calculate the exact timings of the autumnal equinoxes
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between the Gregorian years 13201 BCE and 17191 CE (corresponding to the French Republican years -14991
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to 15399). The times were then converted to UT1+00:09:21, the exact local time at the Paris Observatory.
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UT1 was chosen to keep track of the Earth's rotation without having to worry about the issues posed by
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leap seconds in UTC. Note that due to the uncertainty over
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<a href="https://en.wikipedia.org/wiki/%CE%94T_(timekeeping)">ΔT</a> — the difference between UT1 and
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Terrestrial Time (TT) used in the ephemerides — it is theoretically possible for there to be
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inaccuracies when the equinox occurs very close to midnight.</p>
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<p>For more details about how I calculated this calendar, please see
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<a href="https://quantum5.ca/2022/03/09/art-of-time-keeping-part-4-french-republican-calendar/">my blog
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post on the topic</a>. This is the fourth part of a series on time-keeping, and you are highly
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encouraged to read the
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<a href="https://quantum5.ca/2022/02/16/art-of-time-keeping-part-1-years-dates/">first</a>
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<a href="https://quantum5.ca/2022/02/23/art-of-time-keeping-part-2-time/">three</a>
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<a href="https://quantum5.ca/2022/03/02/art-of-time-keeping-part-3-astronomy-equinoxes/">parts</a>
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for a more complete understanding.</p>
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</div>
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</div>
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<div class="card">
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<div class="card-body">
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<h4 class="card-title">What are those names above the Gregorian date?</h4>
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<p>Those are the names of the days in the
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<a href="https://en.wikipedia.org/wiki/French_Republican_calendar#Rural_calendar">rural version of the
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calendar</a>. This was intended to replace the Catholic Church's calendar of saints, as the French
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Revolution wanted to reduce the influence of the church. Every day of the year has a unique name
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associated with the rural economy and these names are supposed to correspond with the season.</p>
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<p>Every <em>quintidi</em> is named after an animal, every <em>décadi</em> is named after an agricultural
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tool, and the remaining days are named after various plants or produce. The only exception is the winter
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month of Nivôse, which has the remaining days named after minerals.</p>
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</div>
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</div>
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<div class="card">
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<div class="card-body">
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<h4 class="card-title">What are those numbers below the Gregorian date?</h4>
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<p>The five (or more) numbers separated by dots is the corresponding
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<a href="https://en.wikipedia.org/wiki/Mesoamerican_Long_Count_calendar">Mesoamerican Long Count
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calendar</a> date. This is commonly known as the “Mayan calendar.” This calendar is not
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available for dates before August 11, 3114 BCE (25 Thermidor -4905).</p>
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</div>
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</div>
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<div class="card">
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<div class="card-body">
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<h4 class="card-title">What is decimal time?</h4>
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<p class="lead">Decimal time is a time system used during the French Revolution that divided the day into 10
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hours, each with 100 minutes, which contained 100 seconds each.</p>
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<p>The result is 100,000 seconds in one day, compared to the 86,400 seconds with the normal 24-hour
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system. This makes it very easy to denote time as a decimal fraction of a day. For example, decimal time
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5:67:72 (around 13:37:31) on January 1, 2000 can be represented as <code>2000-01-01.56772</code>.</p>
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<p>Also note that each decimal hour is 2.4 normal hours, each decimal minute is 1.44 normal minutes, and
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each decimal second is 0.864 normal seconds.</p>
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<p class="text-muted">Copyright © 2022-<%= new Date().getFullYear() %>
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<a href="https://quantum5.ca">Quantum</a>.
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Licensed under <a href="https://www.gnu.org/licenses/agpl-3.0.en.html">GNU AGPLv3</a>.
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Source code available on <a href="https://github.com/quantum5/qcal">GitHub</a>.<br>
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